Godsil-McKay switching and isomorphism

A. Abiad Monge*, A. Brouwer, W. Haemers

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

4 Citations (Web of Science)


Godsil-McKay switching is an operation on graphs that doesn’t change the spectrum of the adjacency matrix. Usually (but not always) the obtained graph is non-isomorphic with the original graph. We present a straightforward sufficient condition for being isomorphic after switching, and give examples which show that this condition is not necessary. For some graph products we obtain sufficient conditions for being non-isomorphic after switching. As an example we find that the tensor product of the grid L(ℓ,m) (ℓ > m>2) and a graph with at least one vertex of degree two is not determined by its adjacency spectrum.
Original languageEnglish
Pages (from-to)4-11
JournalElectronic Journal of Linear Algebra
Publication statusPublished - 1 Jan 2015

Cite this